Chapter 3: Dynamic Macroeconomic Approaches to the Balance ...

Advanced International Macroeconomics and Finance

Chapter 3: Dynamic Macroeconomic Approaches to the Balance of Payments and the Exchange Rate

Miguel Leon-Ledesma and Alexander Mihailov

2Leon-Ledesma and Mihailov, Advanced International Macroeconomics and Finance, Ch. 3

Plan of talk

• introduction1. The rational expectations revolution2. Flexible-price stock approach under perfect foresight: the

monetary model1. the monetary approach to BoP (peg)2. the monetary approach to NER (float) the monetary model

3. Sticky-price models under perfect foresight: Dornbusch (1976)• motivation

for the model

• key elements and assumptions• model equilibrium

and transition paths

• key result: exchange-rate overshooting4. Empirics of the NER and the random walk hypothesis• wrap-up


Aims and learning outcomes

• aims– to distinguish, summarise and interpret the key macroeconomic

approaches to BoP and NER dynamics under perfect foresight– to present and discuss the mechanics and implications of two of

the most influential models in international macroeconomics• learning outcomes

– contrast and compare flow and stock-flow BoP/NER models– derive and interpret

• the automatic (Humean) price-specie-flow mechanism of BoP adjustment• the monetary model

under peg vs. float

– the exchange rate as an asset price– the ‘fundamentals’ vs. the ‘bubbles’ solution for the exchange rate

• the Dornbusch model equilibrium and transition paths in continuous time and the effects of monetary expansion


Expectations and economic behaviour

• behaviour of economic agents is based on expectations concerning

future levels or evolution of relevant

variables or processes

• this fact differentiates social from natural sciences as acknowledged by Evans and Honkapohja (2001):“Modern economic theory recognises that the central difference between economics and natural sciences lies in the forward-looking decisions made by economic agents.” (p. 5)

• expectations influence the time path of the macroeconomy– and vice versa– so this profound two-sided relationship

is a challenge to modellers

• economic theories attributing a major role to expectations can be first seen in Thornton (1802) and Cheysson (1887)


Basic analytical taxonomy of modelling expectations in economics

• perfect foresight: implicit in classical economics, explicit in early RE models endowing agents with superhuman powers:

• Marshall – static (naïve, no-change) expectations:• Cagan (1956) – adaptive expectations:• Muth (1961) – rational expectations as an equilibrium

concept

– the actual stochastic process that a variable follows depends on the forecast rules used by economic agents

– the optimal choice of the forecast rule by each agent is, in turn, conditional on the choices of others

– in effect, RE equilibrium imposes the consistency

condition that each

agent's choice is a best response to the choices by others

pte pt−1

pte pt

pte pt−1

e pt−1 − pt−1e

pt1e Ept1|t or pt1

e Etpt1


The rational expectations revolution

• Muth (1961) on rational expectations– “Rational Expectations and the Theory of Price Movements”,

Econometrica 29 (3, July)

– introduces (to the economics profession)• the concept

of rational expectations (RE)• and the (minimum) necessary mathematics to implement it

– RE imply that• agents forecast

in a way that is internally consistent with the model generating the variable(s)

whose future behaviour they try to predict• agents are rational in the sense that they

– incorporate all available relevant information (in their information set)– and do not make systematic errors in

their predictions

• the “rational expectations revolution” (in economics)


Classical price-specie-flow mechanism

• classical theory of BoP (that is, CA or TB) adjustment builds on

Hume (1752): automatic price-specie-flow mechanism• if BoP (CA or TB) surplus, TB > 0

– inflow of specie (= gold = money, under the gold standard)

– QTM valid (under flex-price full-employment): Mt

V = Pt

Y => price level ↑

– relative price of exports from surplus country ↑ => demand for exports by

nonresidents ↓– relative price of imports to surplus country ↓

=> demand for imports by

residents ↑– initial BoP (trade) surplus tends to ↓

=> equilibrium restored: TB = 0

• if BoP (CA or TB) deficit, TB < 0: inverse causation applies

• origins of the monetary approach to BoP can be traced back here


Monetary approach: assumptions

1. LOP in goods market (individual

level) => PPP (aggregate

level)2. UIP in asset

(bond) market

3. flexible prices: not fixed, as in the flow approaches to BoP we

studied earlier4. focus on conditions for stock equilibrium in money

market

5. stable money demand function

6. production at the level of full employment => real income fixed7. SOE


Monetary approach to BoP: set-up

1. (credible) peg => money supply is endogenous(ly determined)

2. money demand

arises from transactions motive

3. PPP: goods market equilibrium

4. UIP with static expectations (since peg): capital market

equilibrium

5. money market

equilibrium

mtd − pt y t − t t 0 1 0 t

iid 0,2

MSt ≡ MBt ≡ DCt IRt ≡ EMSt EMBt

≡ EIRt EMBt

pt s pt∗

t t∗ Et St1 St S const for any t (hence ln EtSt1 St

ln 1 0)

1 − dt ir t

s pt∗

pt yt −

t∗

t t

mts ≡ 1 − dt ir t


Monetary approach to BoP: key result

• it is clear from key equation above that if SOE experiences any of– positive income growth– declining interest rates– rising prices

demand for nominal money balances will grow

– if it is not satisfied by an accommodating increase of domestic credit, the public will obtain the additional money it desires to hold by selling goods and/or assets abroad, thus running a(n overall) BoP surplus, i.e. an increase

in international reserves (they get paid in FC which they exchange for HC)

– if it is more than satisfied by central bank domestic credit expansion that exceeds it, the public will eliminate the excess supply of money (it does not wish to hold) by spending or investing it abroad and thus running a(n overall) BoP deficit, i.e. a decrease

in international reserves (they pay FC)• hence, money supply

in the monetary model under peg is endogenous, that is,

determined by the above equation

ir t

mtd

s pt∗ yt − t∗ t −1 − dt


Flexible-price models under perfect foresight

• Cagan (1956) on hyperinflation– “The Monetary Dynamics of Hyperinflation”, in Friedman, Milton (ed.),

Studies in the Quantity Theory of Money, Chicago University Press– empirical closed-economy model to study hyperinflation in 7 countries– argued that during a hyperinflation expected inflation swamps

all other

influences on money demand => specified the MDF in a simple

way

• real money balances depend only

on expected inflation• and not

on real income and interest rates as in the conventional

(IS-LM) MDF– adaptive forecasting: expected future inflation depends on lagged

inflation

• the (flexible NER) monetary model Cagan model:

– extended to open economy

– with the conventional MDF

– assuming perfect foresight (as an extreme

form of rational expectations)

– and underpinned with some basic (but ad-hoc) macro-theory

• to read more: Obstfeld and Rogoff (1996), chapter 8


Monetary approach to NER: set-up

1. float => also called the monetary model (of NER) => money supply

exogenous(ly chosen), to equilibrate money markets in

H and F:

2. PPP: goods market equilibrium

3. usual UIP: capital market equilibrium

4. definition of NER fundamentals5. substituting (in PPP) and solving

supply of real balances in H

mt − pt

demand for real balances in H

yt − t

supply of real balances in F

mt∗ − pt

∗

demand for real balances in F

y t∗ − t∗

st pt − pt∗

t − t∗ Etst1 − st

f t ≡ mt − mt∗ − y t − yt

∗

st

≡

11 f t

≡1−

1 Etst1


Monetary approach to NER: key result

• general forward-looking (RE) solution

• no-bubbles solution (TVC)

• rational bubbles

• interpretation: monetary model is a useful first approximation in providing intuition about NER dynamics (asset price); RER?

tiid N0,2 s t st bt

st j0

k∑ 1 − jEtf tj 1 − k1Etstk1

k→lim 1 − kEtstk 00 ≡ 1

1 1 st j0

k∑ 1 − jEtf tj

bt 11− bt−1 t

k→lim 1 − kEt

s tk

0

k→lim 1 − kEtstk

bt

k→lim 1 − kEtbtk bt ≠ 0


Sticky-price models under perfect foresight

• Dornbusch (1976): perhaps the best known OEM example– “Expectations and Exchange Rate Dynamics”, Journal of Political Economy

84 (December)– extension of the (Keynesian) static

Mundell-Fleming model we studied in

Chapter 2 to a dynamic setting under perfect foresight

– very influential model => Mundell-Fleming-Dornbusch tradition/paradigm• among academic circles

involved with open-economy macro• among policy makers

at national and international institutions– summary of technical approach

• ad-hoc

(not optimising!) model, assuming

explicit functional forms (not deriving them from microfoundations!)

• written in continuous

time (but can be “translated” to a discrete

version: see Obstfeld-Rogoff textbook, section 9.2)

• all variables (except interest rates) in logarithms: for any Zz ≡ ln Z


Dornbusch (1976): motivation for model

• stylised facts to explain

– observed large exchange rate volatility after the demise of Bretton-Woods

• much higher than that of underlying fundamentals• needed to be consistent with rational expectations formation

– effects of a monetary expansion• in the short run, an immediate domestic currency depreciation => monetary

expansion seems to account for fluctuations

in the exchange rate and ToT• during the adjustment process, rising prices may be accompanied by an

appreciation => the trend

behaviour of exchange rates and the cyclical

behaviour of exchange rates and prices stand potentially in contrast• during the adjustment process, there is also a direct effect of the exchange rate

on domestic inflation => the exchange rate as a critical channel for the transmission

of monetary policy to AD for domestic output– differential speed of adjustment of asset

vs goods

markets

which was becoming an interesting novel

topic for research


Dornbusch (1976): general assumptions

1. SOE =>– the world (nominal) interest rate

is given in the world asset

market ι*

– the world price of SOE’s imports

is given in the world goods

market p*

2. domestic output

is an imperfect substitute for imports

=> demand for H (SOE) and F (RoW) output will be affected by their relative price, s + p* –

p in logs (from PPP-based RER, SP*/P, in levels)

3. (NB!) differential adjustment speed of markets– goods

markets adjust slow relative to

– asset (including exchange rate) markets, which adjust instantaneously

4. (NB!) consistent expectations (formation)– formation of (rational) expectations is consistent– with perfect foresight, i.e., the strongest, extreme

form of RE


Dornbusch (1976): assumptions on capital mobility and NER expectations formation

1. perfect capital mobility– assets denominated in domestic and foreign currency are perfect

substitutes

given a proper premium/discount to offset anticipated NER changes

– equivalently, this is (a form of) UIP:

2. exchange-rate expectations formation– expected

depreciation, x > 0, of current spot NER, s, is assumed proportional

(via a coefficient θ) to its discrepancy w.r.t. long-run NER, (for now taken as known, but later an expression which determines it will be developed):

– Dornbusch (1976) makes the point that• while expectations formation, as assumed, may appear ad hoc• it will be consistent with perfect foresight

(to be shown further down)

∗ x

s const

x s − s


Dornbusch (1976): assumptions on money market structure and equilibrium

1. conventional money demand function a monetary model2. money supply /stock/ exogenous(ly given, by SOE’s CnBk)3. (NB!) real income (or output, or AS) is fixed at its full-

employment level, y (initially ↔ variable

output later)

4. money market equilibrium:=> money demand

can be written as

=> relationship linking spot and LR NER with price level

5. stationary money supply process: long-run equilibrium

would imply and hence, through UIP

=> an expression for the long-run

equilibrium price level

ms md mm − p − y − 1

m − p y

p − m −y ∗ s − s

p m − y ∗s s ∗


Dornbusch (1976): key equation on the relationship b/n the NER and the price level

•• solving it for p

determines asset market equilibrium, to be

graphically represented later as the QQ

schedule:

• interpretation of key equation: for given LR values , the

spot NER s can be determined as a f-n of the current price level p

– given the price level p, we have a domestic interest rate from MDF and

an interest rate differential from UIP determined endogenously– given also

the LR NER , from expected depreciation eq. there is a unique

level of the spot NER s such that expected depreciation x

matches the

interest differential– so p↑

=> (from MDF) ↑

=> an incipient capital inflow

=> (from UIP and

expected depreciation eq.) s↓ (appreciation) to the point where the

anticipated depreciation x offsets exactly

the increase in

s s − 1 p − p

p p − s − s p − s s

− ∗

s and p

s

− ∗


Dornbusch (1976): assumptions on goods market structure and equilibrium

1. the foreign price level normalised

so that

the relative price of domestic goods becomes2. a special, ad-hoc

demand f-n for domestic output

3. a special, ad-hoc f-n for the rate of increase of the price of

domestic goods: proportional to an excess demand measure

4. with the relevant LR assumptions and and further substituting for above from MDF, solving

for s

yields

the LR equilibrium NER:

p∗ ≡ lnP∗ ln1 0s − p

lnD u s − p y −

p ln D

Y lnD −≡y

lnY u s − p − 1y −

p 0 ∗

∗

s p∗ − p

s p 1

∗ 1 − y − u


Dornbusch (1976): price level and NER dynamics

• now the earlier price adjustment eq. can be simplified using the LR NER to substitute in it as well as UIP and expected depreciation eq. to express =>

• recall that a 1st-order linear homogeneous differential eq. of some f-n of time z(t), , has a (definite) s-n of the form

• solving, by analogy, the price eq. above yields• substituting in key NER eq.: • interpretation

– the spot NER will converge to its LR level

– NER will appreciate if prices are initially below

their LR level, and conversely

x − ∗ s − sp −

p − p −p − p ≡

≡z

dzdt cz 0 zt z0e−ct

pt p p0 − p e−t

st s − 1 p0 − p e−t s s0 − s e−t


Dornbusch (1976): graphical analysis of model equilibrium and transition paths

• F1 next• the QQ schedule describes asset (here also money) market equilibrium

and has a

negative slope (as can be checked earlier), so it must intersect the 450-line

• the schedule shows all combinations of price levels and exchange rates for which the goods market and the money market clear: can be derived from the eq. with and the MDF:

• solving for p, • the slope

is , hence must intersect the 450-line too => model

equilibrium => model transition paths (F1 next)

p 0p

p

0 u s − p − 1y −

, from MDF

m−p−y−

p u

s m −1−

y

p 0

0 1

p 0


F1 - Dornbusch model: long-run equilibrium and transition paths Source: Authors, based on Dornbusch's (1976) original Figure 1, p. 1166

QQ

A

450 linep

ssLRsC sB

pC

pLR

0

B

0=p&C

pB


Dornbusch (1976): consistent expectations

• if the expectations formation process in expected depreciation eq., driven by θ, must correctly

predict – in compliance with perfect foresight – the actual

path of exchange rates, determined by ν, it must be true that• hence,• the consistent expectations coefficient, , is obtained as the (positive and

stable) solution to the quadratic equation implied by the above expression:

• gives the rate at which Dornbusch (1976) economy will converge to long- run equilibrium along the perfect foresight path: of interest because this assumption

– is not arbitrary– does not involve persistent prediction errors

• for any given price adjustment parameter π, convergence will be faster

– the lower

the interest-rate response of money demand, λ– and the higher

• the interest-rate response of goods demand, σ• and the price elasticity of demand for domestic output, δ

,,,

2

2

2

≡


Dornbusch (1976): graphical and analytical account of NER overshooting

• F2 next– a two-stage adjustment

which implies exchange rate overshooting: a

phenomenon whereby the spot exchange rate temporarily exceeds its long- run value, illustrated by the short-run equilibrium at point B

in Figure 2

– to better understand the key model result, let us also derive it analytically• totally differentiate MDF, noting that p

is instantaneously fixed and y

is always fixed

• in the LR, an ↑

in money causes an equiproportionate

↑

in prices and the exchange rate:

• totally differentiate UIP eq. while holding constantand use in expected depreciation eq. to obtain

• use this to eliminate in liquidity effect

eq. above and solve for

ddm − 1

0

d s d p dm

d s dm∗ d

d sdm −ds

d dsds 1 1

d sdm 1 1

1 ds d s


F2 - Dornbusch model: Exchange Rate Overshooting Source: Authors, based on Dornbusch's (1976) original Figure 2, p. 1169

QQ

B’

AQ’Q’

450 linep

ssLR s’LR sSR

p’LR

pLR

0

B

1

2 0=p&0'=p&

overshooting


Meese and Rogoff (1983): the exchange rate disconnect puzzle

• earlier models imply a semi-reduced form specification

• they estimated the following VAR specification

• criteria to judge and compare forecast performance

s a0 a1m − m∗ a2y − y∗ a3 − ∗ a4e − e∗ a5tb a6tb∗ u

st a1st−1 a2st−2 . . .anst−n B1′ Xt−1 B2

′ Xt−2 . . .Bn′ Xt−n ut

ME ≡Nk−1

q0∑ Ftqk −Atqk

Nk

MAE ≡Nk−1

q0∑ |Ftqk−Atqk|

Nk

RMSE ≡Nk−1

q0∑ Ftqk −Atqk 2

Nk


T1 – The Meese-Rogoff results Source: Meese and Rogoff (1983), Table 1, p. 13, slightly shortened by the authors

Random Forward Univariate VAR Monetary Dornbusch Complete

Model: walk rate AR model model eq. (41)

Exchange Horizon

rate (months)

$/DM 1 3.72 3.20 3.51 5. 40 3. 17 3.65 3.50

6 8.17 9.03 12.40 11.83 9. 64 12.03 9.95

12 12.98 12.60 22.53 15.06 16.12 18.87 15.69

$/yen 1 3.68 3.72 4.46 7. 76 4. 11 4.40 4.20

6 11.58 11.93 22.04 18.90 13.38 13.94 11.94

12 18.31 18.95 52.18 22.98 18.55 20.41 19.20

$/£ 1 2.56 2.67 2.79 5. 56 2. 82 2.90 3.03

6 6.45 7.23 7.27 12.97 8. 90 8.88 9.08

12 9.96 11.62 13.35 21.28 14.62 13.66 14.57

trade- 1 1.99 n.a. 2.72 4. 10 2. 40 2.50 2.74

weighted 6 6.09 n.a. 6.82 8. 91 7. 07 6.49 7.11

$ NEER 12 8.65 14.24 11.14 10.96 11.40 9.80 10.35


Explaining the Meese-Rogoff results

• reaction to the Meese-Rogoff results– has become a subdiscipline within international macroeconomics in itself– exchange rate forecasting is not only a potentially useful tool for

investors seeking to gain returns from currency trading– but a way of testing the validity of fundamentals-based models of

exchange rate determination• the way Meese and Rogoff obtain forecasts of exchange rates

using fundamentals is not a proper out-of-sample forecast– as they used the actual values of fundamentals instead of their forecasts– this led to the appearance of true out-of-sample forecast exercises, of

which Mark (1995) is perhaps the best exponent– he presented evidence of long-horizon predictability based on ideas

coming from the theory of integration and cointegration


T2 – Long-horizon forecasts Source: Authors’ own calculations of Theil’s U=RMSEf/RMSERW. Money is M1

and output is GDP. Data from IMF’s IFS database for 1974:1-2001:3.

Country Canada Japan UK

Horizon

1 0.998 0.981 1.000

6 1.014 0.955 0.976

12 1.033 0.939 0.938

16 1.009 0.847 0.889


Engel and West (2005): the exchange rate as a near-random walk

• Engel and West (2005) take a different route• claim that

– exchange rates and fundamentals are linked in a way– still broadly consistent with asset-pricing exchange rate models

• the exchange rate– should be good predictor of future evolution of fundamentals– as they reflect market participants’ expectations about the future stream of

fundamentals• to test this hypothesis

– they present Granger-causality tests b/n fundamentals and exchange rates

– for the G7 countries and for different measures of fundamentals

Δf t i1

d∑ iΔf t−i

i1

d∑ iΔst−i t


Exchange rate empirics: where do we stand?

• several facts accumulating since Meese and Rogoff1. exchange rate models appear to beat the random walk at forecast horizons

beyond one year2. in-sample fit of exchange rate models is satisfactory3. in periods of current and/or expected high inflation (especially for

emerging markets) exchange rate models have proven extremely useful4. exchange rates seem to contain significant information about the future

evolution of fundamentals (Rossi, 2007)5. fundamentals are good predictors of exchange rates for so-called

‘commodity currencies’ pertaining to the Australian, Canadian, and New Zealand dollars (Chen and Rogoff, 2003)

6. ample evidence that news about macroeconomic fundamentals affect exchange rates in a manner that is compatible with theoretical predictions


Concluding wrap-up

• What have we learnt?– distinguish and discuss

• rational expectations and perfect

foresight

• flexible-price vs. sticky-price models of exchange rate dynamics– derive and interpret the monetary

approach under both peg

and float– derive and understand Dornbusch (1976) model

• equilibrium and transition paths

• effects of monetary expansion– when and why NER overshooting occurs– when and why NER overshooting needs not necessarily occur

– analyse the basic set-up of ad-hoc dynamic monetary OEMs• Where we go next

– to the microfoundations of BoP and exchange rate models– in particular to modelling the dynamics of the current account within the

intertemporal approach to it

Chapter 3: Dynamic Macroeconomic Approaches to the Balance ...

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